21-14t find the factor
1 answer:
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We have been given the function
We know that the range is set of y values for which the function is defined. Therefore, we will find the value for x and then observe the restriction is y's values.
Now, we know that logarithm function is not defined for negative values. Hence, the value for y is always greater than zero.
Therefore, the range of the function is given by y>0
B is the correct option.
We have been given a graph of function g(x) which is a transformation of the function
Now we have to find the equation of g(x)
Usually transformation involves shifting or stretching so we can use the graph to identify the transformation.
First you should check the graph of
You will notice that it is always above x-axis (equation is x=0). Because x-axis acts as horizontal asymptote.
Now the given graph has asymptote at x=-2
which is just 2 unit down from the original asymptote x=0
so that means we need shift f(x), 2 unit down hence we get:
but that will disturb the y-intercept (0,1)
if we multiply by 3 again then the y-intercept will remain (0,1)
Hence final equation for g(x) will be:
